A United Nations economist was arrested on Tuesday on charges that he brought a household worker from Bangladesh to New York, where he underpaid and overworked her and also took steps to cover up his scheme.

The economist, Hamidur Rashid, a Bangladeshi, had obtained a special visa for the employee after submitting a signed contract to the United Nations stating that he would pay her $420 for a 40-hour workweek, or $10.50 an hour, according to a criminal complaint unsealed in Federal District Court in Manhattan.

The contract said Mr. Rashid, 50, would also pay the woman, who had once worked in his home in Dhaka, Bangladesh, for overtime hours and not charge her for food or lodging, the complaint added.

But Mr. Rashid then had her sign a second contract that said she would be paid only $290 a week, or $7.25 an hour, and that he could deduct up to $75 per week from her salary for food and lodging, the authorities said.

At various times, the complaint said, Mr. Rashid told the woman that if she worked for someone else, she would “go to jail and then back to Bangladesh.”

Ultimately, Mr. Rashid did not pay the woman directly; rather, he paid her husband in Bangladesh the equivalent of $600 for each month she worked, which came to about $3.49 an hour, the complaint said.

The case was not the first in which federal charges have accused a diplomat of mistreating a domestic employee, with perhaps the most prominent episode involving an Indian diplomat who was allowed to return home in 2014 without facing trial in the United States. Her arrest had spurred sharp criticism of the United States by some Indian officials and heightened tensions between the two countries.

Mr. Rashid, though, does not represent his government. He is employed by the United Nations, which contends that diplomatic immunity does not absolve its employees from the need to obey United States laws.

“It’s important to keep in mind that issues of immunities would not apply here,” the United Nations spokesman, Stéphane Dujarric, said.

The complaint says that Mr. Rashid “enjoys limited diplomatic immunity with respect only to those acts undertaken in his official capacity” and “this conduct” was not within his official capacity. Among the charges against him are visa fraud and fraud in foreign labor contracting.

The woman, who was not identified, entered the United States in January 2013 and worked for Mr. Rashid in his home in Manhattan until October 2013, the complaint said.

Joon H. Kim, the acting United States attorney in Manhattan, said that Mr. Rashid “took cruel advantage of his position of power.”

Mr. Rashid once served as the coordinator of a program for the legal empowerment of the poor at the United Nations Development Program. In his current capacity as an economist for the Department of Economic and Social Affairs, he wrote papers warning of the economic slowdown in developing countries, including one, published in HuffPost, with the Columbia University economist Joseph E. Stiglitz.

A United Nations biography says Mr. Rashid worked in his country’s foreign ministry and describes him as “a catalyst” in Bangladesh’s accession to the United Nations Convention Against Corruption and the establishment of the National Human Rights Commission of Bangladesh.

Christopher A. Flood, a lawyer for Mr. Rashid, declined to comment.

A version of this article appears in print on , on Page A20 of the New York edition with the headline: U.N. Worker Is Charged In Fleecing Of Home Aide. Order Reprints | Today’s Paper | Subscribe